If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by the function , where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the volume makes physical sense?
A)0

Question

If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by the function  , where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the volume makes physical sense? ​
A)0 < x < 44 
B)-44 < x < 0 
C)0 < x < 22 
D)0 < x < 2 
E)-2 < x < 2

Quizplus · Accepted Answer

The volume of the box cannot be negative and since x is a length, it cannot be negative either. Therefore, the domain must be restricted to positive values of x. Additionally, if x is too large, the box may be too big to be handled by the delivery service. From the given function, we can find that the maximum volume occurs when x = 22. Therefore, the domain of x must be 0 < x < 22.

If a Box with a Square Cross Section Is to Be